by khongphaiwminh, May 6, 2025, 4:31 PM 
that satisfy the equation
for any 
. Note that 
.by nataliaonline75, May 6, 2025, 4:31 PM 
non-negative real numbers, then we have:
by Jackson0423, May 6, 2025, 3:36 PM 
be a set consisting of non-negative integers such that:
,
, both 
and 
..by MathsII-enjoy, May 5, 2025, 3:22 PM 
| 
with 
are positive integers and 
is prime (
), we get: 
by Jackson0423, May 5, 2025, 1:27 PM 
such that![\[
f\left(\frac{x^2 - f(x)}{f(x) - 1}\right) = x
\]](http://latex.artofproblemsolving.com/8/0/0/8009a4709ffd6708023d67db2b544e605d1fbe68.png)
for all real numbers 
satisfying 
.by KAME06, Feb 28, 2025, 11:43 PM 
such that 
and:
by Kayak, Jul 17, 2019, 12:31 PM 
be an acute-angled scalene triangle with circumcircle 
and circumcenter 
. Suppose 
. Let 
be the orthocenter and 
be the incenter of triangle . Let 
be the midpoint of the arc 
of the circumcircle of triangle 
, containing .
be a point on the arc 
of not containing 
, such that 
. Let 
be the circumcenter of triangle 
. Prove that the lines 
and 
meet on .by shobber, Apr 8, 2006, 3:45 AM 
and 
such that![\[ {a^2+b\over b^2-a}\quad\mbox{and}\quad{b^2+a\over a^2-b} \]](http://latex.artofproblemsolving.com/e/3/b/e3bc96af9f635e1c10e21dc91894c8afbf113a6d.png)
by orl, Oct 22, 2004, 2:59 PM 
of positive integers such that 
is divisible by 
.
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